Roe dissipation coefficients
After physical fluxes and absolute eigenvalues (with optional Harten fix) are known, the Roe scheme subtracts a dissipative correction built from wave coefficients and jumps in conserved variables.
Wave coefficients
\[\xi_1 = \frac{2\tilde{a}_1 - \tilde{a}_2 - \tilde{a}_3}{2 c^2},\qquad
\xi_2 = \frac{\tilde{a}_2 - \tilde{a}_3}{2 c}\]
where \(\tilde{a}_i\) are the entropy-fixed absolute eigenvalues.
Continuity / normal mass jump used in the energy coupling:
\[d_c = v_n\,\Delta\rho - \mathbf{n}\cdot\Delta(\rho\mathbf{v})\]
Conservative to primitive (5-eq)
\[\rho = |q_\rho|,\quad
\mathbf{v} = \mathbf{q}_{\rho v}/\rho,\quad
p = (\gamma-1)\big(q_E - \tfrac12\rho|\mathbf{v}|^2\big)\]
Pure APIs: RoeDissipationWaveCoefficients, RoeContinuityNormalJump,
IdealGasConservativeToPrim (NsInvFluxPolicy.h).
Tests: inv_flux_policy_test.
Total-enthalpy jump
\[\Delta H = -(\gamma-1)\big(\mathbf{v}\cdot\Delta(\rho\mathbf{v}) - \Delta(\rho e)\big)
+ \tfrac12(\gamma-1)|\mathbf{v}|^2\,\Delta\rho\]
Coupling terms and five-equation write-back
\[\mathrm{term}_1 = \Delta H\,\xi_1 + d_c\,\xi_2,\qquad
\mathrm{term}_2 = c^2 d_c\,\xi_1 + \Delta H\,\xi_2\]
\[\mathbf{F} \leftarrow \mathbf{F}
- \big(\tilde{a}_1\Delta\mathbf{q} - \mathbf{r}(\mathrm{term}_1,\mathrm{term}_2)\big)\]
with the standard Roe right-eigenvector combination encoded in
ApplyRoeDissipationFiveEq.